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Algorithmica

, Volume 76, Issue 4, pp 1245–1263 | Cite as

An FPTAS for the Volume Computation of 0-1 Knapsack Polytopes Based on Approximate Convolution

  • Ei AndoEmail author
  • Shuji Kijima
Article

Abstract

Computing high dimensional volumes is a hard problem, even for approximation. Several randomized approximation techniques for #P-hard problems have been developed in the three decades, while some deterministic approximation algorithms are recently developed only for a few #P-hard problems. Motivated by a new technique for a deterministic approximation, this paper is concerned with the volume computation of 0-1 knapsack polytopes, which is known to be #P-hard. This paper presents a new technique based on approximate convolutions for a deterministic approximation of volume computations, and provides a fully polynomial-time approximation scheme for the volume computation of 0-1 knapsack polytopes. We also give an extension of the result to multi-constrained knapsack polytopes with a constant number of constraints.

Keywords

Approximate convolution Volume computation #P-hard  Knapsack polytope 

Notes

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments. This work is partly supported by Grant-in-Aid for Scientific Research on Innovative Areas MEXT Japan “Exploring the Limits of Computation (ELC)” (Nos. 24106008, 24106005).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Sojo UniversityKumamotoJapan
  2. 2.Kyushu UniversityFukuokaJapan

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